deletions | additions       diff --git a/RDMFT1.tex b/RDMFT1.tex  index b801149..db8a141 100644  --- a/RDMFT1.tex  +++ b/RDMFT1.tex 
...
\end{eqnarray}  where the natural orbitals $\phi_i(\mathbf{r})$ and their occupation numbers $n_i$ are the eigenfunctions and eigenvalues of the 1-RDM, respectively.  As in the case of DFT, the exact functional of RDMFT is unknown. Different approximate functionals are employed and minimized with respect to the 1-RDM in order to find the ground state energy.   In RDMFT the total energy is given by   \begin{eqnarray}  E=\sum_{i=1}^\infty\int d\mathbf{r} n_{i}\phi^{*}_{i}(\mathbf{r})\left(-\frac{\nabla^2}{2}\right) \phi_{i}(\mathbf{r})+\sum_{i=1}^\infty \int d\mathbf{r} V_{\mathrm{ext}}(\mathbf{r})n_{i}|\phi_{i}(\mathbf{r})|^{2}\nonumber\\  +\frac{1}{2}\sum_{i,j=1}^\infty n_{i} n_{j}\int d\mathbf{r} d\mathbf{r'} \frac{|\phi_{i}(\mathbf{r})|^{2} |\phi_{j}(\mathbf{r})|^{2}}{|\mathbf{r}-\mathbf{r'}|} + E_{xc}\left[\{n_{j}\},\{\phi_{j}\}\right]\label{eqenergy}  \end{eqnarray}  As in the case of DFT,  the exact functional of RDMFT is unknown. The  part that needs to be approximated $E_{xc}[\gamma]$ comes only from the interaction term (contrary to KS-DFT), as the interacting kinetic energy can be explicitely expressed in terms of $\gamma$. Different approximate functionals are employed and minimized with respect to the 1-RDM in order to find the ground state energy.  A common approximation for $E_{xc}$ is the M\"uller, M\"uller functional,  which has the following form \begin{eqnarray}  E_{xc}(\{n_j\},\{\phi_j\})=-\frac{1}{2}\sum_{i,j=1}^\infty \sqrt{n_{i} n_{j}}\int d\mathbf{r} d\mathbf{r'} \frac{\phi_{i}^{*}(\mathbf{r})\phi_i(\mathbf{r'}) \phi_{j}^{*}(\mathbf{r'})\phi_j(\mathbf{r})}{|\mathbf{r}-\mathbf{r'}|}  \end{eqnarray}